Due Mar 23, 3:59 AM EDT
These two graphs are not isomorphic.

Which graph parameters differ for these two graphs?
The numbers of edges are different: 7 and 5.
The second graph is acyclic (it is a tree), while the first one is not.
These two graphs are isomorphic.

In an isomorphism between them, which vertex of the second graph corresponds to the green vertex of the first one.
This vertex can be described, in both graphs, as "the vertex which is connected to the vertex with one outgoing edge".
These two graphs are isomorphic.

How many isomorphisms are there between them? An isomorphism is a way of establishing a one-to-one correspondence between vertices of the left graph and vertices of the right graph, such that two vertices are connected on the left if and only if the corresponding vertices are connected on the right.
An isomorphism should map the (unique) vertex with one outgoing edge to the vertex with one outgoing edge, and the vertex with three outgoing edges to the vertex with three outgoing edges. Thus, the only free choice left is how to map two remaining vertices.